Title of the talk: Flow, transport and mechanics in fractured porous media.
In this talk, we review the theory, simulation technology and physical validation of so-called mixed-dimensional models for flow in, and deformation of, fractured porous media.
The key component of mixed-dimensional models is the representation of fractures and their intersections as lower-dimensional objects. This gives rise to a rich mathematical setting, where techniques from differential geometry must be combined with classical continuum mechanics and numerical analysis. We will give an overview of some of the main results in this direction, providing mixed-dimensional models with a solid theoretical foundation.
At the same time, several concerns can be raised about the practical applicability of such mixed-dimensional models, and in particular their validation as compared to real-world flows. We will discuss what we believe is the first qualitative validation of mixed-dimensional models in terms of a manufactured fractured rock. In our experiments, radioactive tracer was injected and imaged by a high-resolution multimodal PET-CT scanner. We particularly elaborate the development of new analysis tools for flows in porous media that we have developed to allow for direct quantitative comparison between experiment and simulation.
Short bio: Jan Martin Nordbotten was the youngest ever to complete a PhD in Norway, and the third-youngest professor. He is currently part of the porous media research group in the Department of Mathematics at the University of Bergen. Nordbotten is a recipient of both national and international awards for his research, and is a former VISTA professor of the Norwegian Academy of Sciences and Letters. Nordbotten’s publications span the whole spectrum of applied mathematics, including both theoretical and numerical methods. His research is applied to topics as diverse as ecohydrology, evolution, medical imaging, porous media and renewable energy.
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